**4. Faceted crystal growth**

110 Recent Advances in Crystallography

squares was 50 nm.

**3.4. Packing of Lipid A-phosphates** 

the above-mentioned icosahedral quasicrystal with a different length scale. The tiling pattern of triangles (*N3*) and squares (*N4*) where the vertices were surrounded by a triangle-square-triangle tiling pattern possessed a *p4gm* plane group. Another coded Lipid A-diphosphate approximant showed an 8/3 ratio with 6-fold symmetry and plane group *p6mm*. Both (3.3.4.3.4) and dodecagonal phases revealed a *N3/N4* ratio of approx. 2.34; the ratio of the p6mm plane group was 8/3. Because bond orientational order existed, the direction of domains was classified into three orientations for the (3.3.4.3.4) tiling, but only two for the 8/3 approximants. The average magnitude of the prominent scattering vectors, ׀Q׀ = 0.121 nm-1, and the length of sides of the triangles and of the

Under the assumption that the macroscopic shape of a crystal is related to its microscopic symmetry and taking the various X-ray diffraction patterns, the SAED's and the morphology into consideration, the Lipid A-diphosphate structures and their approximants can be reconciled by lowering the symmetry from cubic, *Im* 3 *m* or *Ia* 3 *d* (*a* = 4.55 nm) for the diphosphate or monophosphate, respectively, to rhombohedral *R* 3 *m*, and finally to monoclinic (P21 or C2) which is acceptable if the Lipid A-phosphate anions were completely orientationally ordered [12]. This could be attributed to two different space-filling packings: (i) two dodecahedra on site **a** and six tetrakaidecahedra on site **d**, forming a *Pm* 3 *n* lattice; (ii) or sixteen dodecahedra on site **d** and eight hexadecahedra on site **a,** forming an *Fd* 3 *m* lattice (Fig. 8). The space-filling network of Lipid A-diphosphate consisting of slightly distorted polyhedra is reminiscent of the known basic frameworks of gas-hydrates and sodium silicon sodalites. The final geometry of the "spheres", i.e. whether they were rounded or faceted in shapes, was established. The equilibrium separation distance between the interfaces of the "spheres" suggested that they repel each other as a result of electrostatic, steric, van der Waals forces as well as water layer surrounding the spheres. The small cubic *Pm* 3 *n* (*a* = 6.35 nm) structure observed for the Lipid A-monophosphate clusters [38, 48], but different from the large cubic unit cell with *a* = 49.2 nm materialized as a result of a space-filling combination of two polyhedra, a dodecahedra and a tetrakaidodecahedra. This is in contrast to the tetrakaidecahedra (*Im* 3 *m)* or rhombodo-decadecahedra (*Fd3m*) packings observed for the Lipid A-diphosphate assemblies (Fig. 8). The small cubic *Pm* 3 *n* (*a*  = 6.35 nm) structure observed for the Lipid A-monophosphate clusters [38, 48], but different form the large cubic unit cell with *a* = 49.2 nm materialized as a result of a space-filling combination of two polyhedra, a dodecahedra and a tetrakaidodecahedra. This is in contrast to the tetrakaidecahedra (*Im* 3 *m)* or rhombodo-decadecahedra (*Fd3m*) packings observed for the Lipid A-diphosphate assemblies. **Note:** The limited number of reflections observed for this large cubic unit cell in case of the Lipid A-monophosphate was not sufficient to discriminate between primitive and body-centered-cubic lattices, or more precisely between *Pn-n* and *I- - -* extinction groups. The two differ by the reflection condition *hkl: h=k+l=2n*, which satisfied the BCC lattice, but the first set of reflections on which this condition could

#### **4.1. Two-phase coexistence regions in monolayers**

Normally equilibrium thermodynamics prevent faceting in two dimensions (2d) because the one-dimensional perimeter of a two-dimensional crystal exhibits no long-range order at any non-zero temperature. However, the formation of stable facets during crystallization need not prevent faceted crystal growth in two dimensions, which is supported both experimentally [18, 51-53] and by computer simulations [54-56]. This possibility is extremely useful in studies of cell surface recognition in the presence of Lipid A-diphosphate e.g. surface patterning, mechanical properties and cell mechanics with optical tweezers. Moreover, surface tension effects become important as the interface is no longer planar and

#### 112 Recent Advances in Crystallography

it introduces a length scale of the order of a few nm, influencing crystal shape, morphology and stability as well as biomineralization [57].

#### **4.2. Surface-tension-gradient-induced crystal formation in monolayers**

We observed a surface-tension gradient induced crystal growth phenomena in Lipid Adiphosphate and Lipid A-diphosphate approximants layers comprising of the same chemical composition as studied for the re-entrant phase BCC and FCC networks. Briefly, the surface tension gradient was created by heating the trough (1 cm3, 5.0 mins/C), measuring simultaneously the surface tension, , for various *n*, either in the presence of a fluorescent dye (Alexa Fluor 488, Molecular Probes USA) which was spread on the aqueous surface, or by direct observation with a Scanning Electron Microscope (SEM) when the samples were withdrawn from the container under a light microscope (Olympus BX 60) and transferred to a substrate, coated with Pt (1min) and studied in a SEM (JEOL 6400). A video recording system was hooked up to the light microscope for monitoring the morphology changes with time. Double-chained lipids reveal saturation coverage of 1.0 molecule/0.5nm2 in aqueous media, which are magnitudes different from Lipid Adiphosphate where ordering of Lipid A-diphosphate occurs at concentrations that are less than 1.33 x 10-11 mbar·s or saturation monolayer coverage of 10-5 L [58, 59]. The surface density of the dye is 10-2 molecule/nm2. Since *n* is much lower than the CMC of Lipid Adiphosphate (14.0 g/mL (3.5 x 10-5 mM) at 10C and 7.5 g/mL at 20C (2.0 x 10-5 mM; Kraft point 5.8C), the dye does not dissolve in the bulk phase, and because the measurements are far from the stability region of the Lipid A-diphosphate 3d crystals, the surface film is 2 dimensional. By compressing the monolayer film a liquid phase-liquid condensed phase coexistence space is reached. The coexistence phase is characteristic of the formation of dark and fractal like liquid condensed phase domain when viewed through the fluorescent microscope. The morphology of the various 2d Lipid A-diphosphate images and their evolution are depicted in Figure 9.

Faceted domains built up on the tip of the fractal branches, but these tips are not stable and after continuous crystal growth a dendritic pattern evolved. The domains are squeezed in-between the dendritic stems promote to grow. However, the external tips of the domains have a higher probability to expand into a dendritic pattern. It appears that the hexagonal shaped Lipid A-diphosphate crystals grew in the liquid-crystalline boundary (Fig. 9). It was also observed that the hexagonal domains enlarged to the dendritic pattern, where the corners of the hexagons are very sharp and the dendrites revealed stable tips and strong stems are clearly observed. Quantitatively, the Lipid Adiphosphate is higher than in the middle of the straight edge at the corners of the faceted pattern. This implies that the main transfer rate to the corners is higher than at other places in space causing an instability region. As a result the crystal edge corners grew more rapidly than the center region and (curled) dendrites appeared on the corners of the hexagon (Fig. 9g).

Mineralization of Lipid A-Phosphates in Three- and Two-Dimensional Colloidal Dispersions 113

112 Recent Advances in Crystallography

and stability as well as biomineralization [57].

evolution are depicted in Figure 9.

hexagon (Fig. 9g).

it introduces a length scale of the order of a few nm, influencing crystal shape, morphology

We observed a surface-tension gradient induced crystal growth phenomena in Lipid Adiphosphate and Lipid A-diphosphate approximants layers comprising of the same chemical composition as studied for the re-entrant phase BCC and FCC networks. Briefly, the surface tension gradient was created by heating the trough (1 cm3, 5.0 mins/C), measuring simultaneously the surface tension, , for various *n*, either in the presence of a fluorescent dye (Alexa Fluor 488, Molecular Probes USA) which was spread on the aqueous surface, or by direct observation with a Scanning Electron Microscope (SEM) when the samples were withdrawn from the container under a light microscope (Olympus BX 60) and transferred to a substrate, coated with Pt (1min) and studied in a SEM (JEOL 6400). A video recording system was hooked up to the light microscope for monitoring the morphology changes with time. Double-chained lipids reveal saturation coverage of 1.0 molecule/0.5nm2 in aqueous media, which are magnitudes different from Lipid Adiphosphate where ordering of Lipid A-diphosphate occurs at concentrations that are less than 1.33 x 10-11 mbar·s or saturation monolayer coverage of 10-5 L [58, 59]. The surface density of the dye is 10-2 molecule/nm2. Since *n* is much lower than the CMC of Lipid Adiphosphate (14.0 g/mL (3.5 x 10-5 mM) at 10C and 7.5 g/mL at 20C (2.0 x 10-5 mM; Kraft point 5.8C), the dye does not dissolve in the bulk phase, and because the measurements are far from the stability region of the Lipid A-diphosphate 3d crystals, the surface film is 2 dimensional. By compressing the monolayer film a liquid phase-liquid condensed phase coexistence space is reached. The coexistence phase is characteristic of the formation of dark and fractal like liquid condensed phase domain when viewed through the fluorescent microscope. The morphology of the various 2d Lipid A-diphosphate images and their

Faceted domains built up on the tip of the fractal branches, but these tips are not stable and after continuous crystal growth a dendritic pattern evolved. The domains are squeezed in-between the dendritic stems promote to grow. However, the external tips of the domains have a higher probability to expand into a dendritic pattern. It appears that the hexagonal shaped Lipid A-diphosphate crystals grew in the liquid-crystalline boundary (Fig. 9). It was also observed that the hexagonal domains enlarged to the dendritic pattern, where the corners of the hexagons are very sharp and the dendrites revealed stable tips and strong stems are clearly observed. Quantitatively, the Lipid Adiphosphate is higher than in the middle of the straight edge at the corners of the faceted pattern. This implies that the main transfer rate to the corners is higher than at other places in space causing an instability region. As a result the crystal edge corners grew more rapidly than the center region and (curled) dendrites appeared on the corners of the

**4.2. Surface-tension-gradient-induced crystal formation in monolayers** 

**Figure 9.** Development of fractal crystalline pattern of Lipid A-diphosphate domains as a function of time. The video-recorded light-optical microscopy images were directly converted to black and white images by using the Adobe Photoshop (version 8.0.1.) (**a)** Observed fractal patter when the monolayer of Lipid A-diphosphate is compressed to the liquid-crystalline to liquid-expanded coexistence region**. (b) – (e)** show the time evolution of the same Lipid A-diphosphate pattern from fractal to dendritic behavior under the microscope. At the tips (red arrows) in **(b & c)** become thicker and reveal facets; normally these tips grow into thick dendrites with clearly main stem, strong and stable tips **(d & e).** The bar size is 50 m. The morphologies of the liquid-crystalline domains of Lipid A-diphosphate are shown **(f-i).** In **(f)** a HRTEM image of faceted cubic-like and unconnected Lipid A-diphosphate crystals are shown (the bar is 100 nm). **(g)** depicts the observed hexagon domain which grows usually near the cubic-like crystal domain; but this is dependent on T, however, at constant *I*; the bar size is 10 nm*.* **(h)** Shows a SEM image of fusing Lipid A-diphosphate crystals observed when the monolayer expands to a fluid state, or compresses to a certain density dc where the crystals contact one another and fuse. The bar is 10 m, T = 295 K and c *=* 6.0 g/mL. **(i)** Shows single Lipid A-diphosphate nanocrystals grown at T = 295 k but in c *=* 60.0 g/mL and in the presence of 20 M NaOH. These nanocrystals exhibit icosahedral faces and also rhombic triacontahedral faceting; the bar size is 1 m.

For this instability, a field gradient existed where crystals grew faster as they reached deeper into the gradient. As a result of this instability was an invasion of the more viscous phase by the less viscous phase without ordering or a characteristic length scale. It was also a process which operated during diffusion-limited aggreagtion, in which case the diffusive instability led to a fractal structure. Moreover, in the growth process far from equilibrium the aggregation of the fractal-like domains can be faster than the relaxation process of the Lipid A-diphosphate clusters. Hence the Lipid A-diphosphate clusters form rectangular lattices. The 2d-hexagonal domains nucleated and grew under lower force, where in the meantime the Lipid A-diphosphate clusters gain enough time to relax to minimum lattice energy positions. Therefore, the difference in macroscopic morphology together with the caused instability implies that, the structure of the liquid crystal domains depend on the driving force. Also what should be mentioned is the influence of different chiral conformers in the bulk solution whose presence has been supported by circular dichroism experiments and molecular simulations (unpublished results, 2011). The observed hexatic phase (Fig. 10), which separates the isotropic liquid Lipid A-

diphosphate cluster phase and the liquid crystalline phase has short-range translational and quasi long-range orientational order.

In accord with theory [22, 60-64] we are able to detect three phases: a liquid, hexatic and a crystal Lipid A-diphosphate phase, but no fluid-crystal or hexatic-crystal phase coexistence phase. This is supported from surface tensiometry measurements as a function of T and g/mL bulk concentration revealing hexagonally shaped crystals.

**Figure 10.** SAED's (Joel, T 3010, 300 kV, 15 cm) and SAXS images for the various crystalline Lipid Adiphosphate clusters at different M NaOH and Lipid A-diphosphate concentrations (*c*). **(A)** SAED for a 2d-pattern, a 10 nm thick layer obtained from very small Lipid A-diphosphate crystallites (sizes 0.1- 0.2 m, c = 3.5 g/ml, T = 295 K and c = 25.5 mN/m in 5 M NaOH. This 2d pattern indicates a hexagonal or centered trigonal unit cell with a = 3.70 nm. The bar size is 0.5 nm-1, and the image was obtained with a CCD camera. **(B)** Enlarged SAED pattern of a 2d crystallite for c = 8.5 g/ml, Tc = 295 K and c = 25.5 mN/m but for 5.75 M NaOH. This crystalline Lipid A-diphosphate material is maintained for approximately 1-1.5 h., and is indicative for the hexatic phase (inset). **(C)** SAXS pattern for the fluid phase where only diffuse rings but no dots are visible and close to the melting line; a change from solid to liquid occurred (*d/dT* 0, Ss Sb) where Ss is larger than the bulk entropy (Sb) and where the density is very similar to that of the bulk (for T Tc).

Normally, lipids or surfactant concentrations are well in the range of mM (mg/mL) when forming a liquid-like monolayer, but in the case of Lipid A-diphosphate we are in the g/ml range or lower and strongly dependent on polydispersity in charge and size distribution! This is significantly different from insoluble surfactant monolayers. Preliminary theoretical fitting results of the thermodynamics, (T) vs. T (T Tc), with Tc is the critical temperature where the slope changed (*d*/*d*T)*c*, yielded values for the chain interactions of *b* 41.8 kBT and the effective sugar-phosphate headgroup attraction of *a* -6.6 kBT [58].

Different phase can be distinguished from 2d structure factors (Fig. 10). The functional form of the angular intensity profile of S(Q) is the square root Lorenzian of the hexatic phase and Lorenzian of the crystal phase [65, 66]. In the hexatic phase both the ring and the six spots (Fig. 10A & B) are clearly noticeable, where the six spots indicate a small ordered patchy like located in the dense liquid Lipid A-diphosphate dispersion (Fig. 10C). Using the disorder parameter D [67, 68], which is a function of T, the solid hexatic phase and the liquid phase reveal different slopes [69]. In the hexatic phase both D and the variance sharply increases with configurational temperature. Approaching the melting region close to the liquid phase the average and the variance of D approaches 5.0 and 4.0, respectively, where Dj = 0 corresponds to a perfect triangular lattice and becomes larger for more disordered structures. The thermal fluctuation and entropic interactions lower the free energy (Eq. 1) of the interface when two Lipid A-diphosphate particles approach each other in a sort of Casimir type of effective attraction [70-72]. The polydispersity influences the coexistence region of the fluid and crystal to higher volume fractions. At fixed supersaturation, the height of the nucleation barrier is not affected by a polydispersity up to 6% in our experimental studies; while for larger polydispersities the barrier increases sharply; thus an increase in surface tension with T and *n* is noticed.

114 Recent Advances in Crystallography

to liquid occurred (*d*

is very similar to that of the bulk (for T Tc).

and quasi long-range orientational order.

g/mL bulk concentration revealing hexagonally shaped crystals.

diphosphate cluster phase and the liquid crystalline phase has short-range translational

In accord with theory [22, 60-64] we are able to detect three phases: a liquid, hexatic and a crystal Lipid A-diphosphate phase, but no fluid-crystal or hexatic-crystal phase coexistence phase. This is supported from surface tensiometry measurements as a function of T and

**Figure 10.** SAED's (Joel, T 3010, 300 kV, 15 cm) and SAXS images for the various crystalline Lipid Adiphosphate clusters at different M NaOH and Lipid A-diphosphate concentrations (*c*). **(A)** SAED for a 2d-pattern, a 10 nm thick layer obtained from very small Lipid A-diphosphate crystallites (sizes 0.1- 0.2 m, c = 3.5 g/ml, T = 295 K and c = 25.5 mN/m in 5 M NaOH. This 2d pattern indicates a hexagonal or centered trigonal unit cell with a = 3.70 nm. The bar size is 0.5 nm-1, and the image was obtained with a CCD camera. **(B)** Enlarged SAED pattern of a 2d crystallite for c = 8.5 g/ml, Tc = 295 K and c = 25.5 mN/m but for 5.75 M NaOH. This crystalline Lipid A-diphosphate material is maintained for approximately 1-1.5 h., and is indicative for the hexatic phase (inset). **(C)** SAXS pattern for the fluid phase where only diffuse rings but no dots are visible and close to the melting line; a change from solid

Normally, lipids or surfactant concentrations are well in the range of mM (mg/mL) when forming a liquid-like monolayer, but in the case of Lipid A-diphosphate we are in the g/ml range or lower and strongly dependent on polydispersity in charge and size distribution! This is significantly different from insoluble surfactant monolayers. Preliminary theoretical fitting results of the thermodynamics, (T) vs. T (T Tc), with Tc is the critical temperature where the slope changed (*d*/*d*T)*c*, yielded values for the chain interactions of *b* 41.8 kBT

Different phase can be distinguished from 2d structure factors (Fig. 10). The functional form of the angular intensity profile of S(Q) is the square root Lorenzian of the hexatic phase and Lorenzian of the crystal phase [65, 66]. In the hexatic phase both the ring and the six spots (Fig. 10A & B) are clearly noticeable, where the six spots indicate a small ordered patchy like located in the dense liquid Lipid A-diphosphate dispersion (Fig. 10C). Using the disorder parameter D [67, 68], which is a function of T, the solid hexatic phase and the liquid phase reveal different slopes [69]. In the hexatic phase both D and the variance sharply increases with configurational temperature. Approaching the melting region close to the liquid phase the average and the variance of D approaches 5.0 and 4.0, respectively, where Dj = 0 corresponds to a perfect triangular lattice and becomes larger for more disordered structures. The thermal fluctuation and entropic interactions lower the free energy (Eq. 1) of

and the effective sugar-phosphate headgroup attraction of *a* -6.6 kBT [58].

*/dT* 0, Ss Sb) where Ss is larger than the bulk entropy (Sb) and where the density

But, when melting of Lipid A-diphosphate crystals commenced above a critical temperature (Tc), c as a function of *n*, the evaporation rate becomes slower when the crystallites shrink. These crystallites may sediment rapidly when transforming into the bulk liquid with a higher density than from the onset of the crystallization, where a lower density of the bulk solution is met than the actual crystal and evaporates swiftly. This melting scenario is reminiscent to the coexistence of a dense and expanded crystal phase. This Lipid Adiphosphate crystal phase also depends strongly on polydispersity in size, mass and charge for T and *n* is constant. The total number of Lipid A-diphosphate crystals depends on the kinetics during the monolayer compression and is a function of *n*, T and . Once the early seed have developed the number of domains is fixed and does not change with subsequent compression unless the monolayer expands to a fluid state, or compresses to a certain density dc where the crystals contact one another and fuse (Fig. 8h). Evidently this depends on the rate of compression (or evaporation) or "impurities" seen as "various Lipid Adiphosphate conformers" present in the bulk Lipid A-diphosphate dispersion due to the conformational changes of the disaccharide as noticed from the crystal structures of Lipid Amonophosphate [73]. The cause of this resulting instability originates from an increase of lipid A-phosphate conformers over another conformer on a characteristic length scale rather than on impurities [74]. It is also a process which operated during diffusion-limited aggreagtion, in which case the diffusive instability led to a fractal structure. Furthermore, the shape of the Lipid A-diphosphate crystals (Fig. 8A) is also affected by the interfacial free energy between the solid and liquid phase. Particularly, the interface influences the free energy penalty A, which is proportional to the area of the interface and the surface energy . Consequently, the free energy difference of the crystal and the fluid is:

$$
\Delta \mathbf{G} = \mathbf{A} \cdot \mathbf{y} - \mathbf{V} \cdot \mathfrak{n}\_{\text{crystal}} \Delta \mu \tag{1}
$$

Where V is the volume of the crystal nucleus, *ncrystal* is the particle number density in the crystal and = Fluid - crystal is the difference of the chemical potential of fluid and crystal, respectively.

Furthermore, the 2d order quality of the Lipid A-diphosphate crystals is influenced by grains due to mixed sizes and shapes (Fig. 9C). Complete uniformity cannot be expected. Assuming the 2d lattice and the force between adjacent spheres (or ellipsoidal particles with a low axial ratio) are identical may yield under compression (sedimentation, gravity, capillary forces) another packing than hexagonal resulting in change to a cubic lattice. This cubic lattice has actually been found for both lipids. Consequently the ordered 2d hexagonal structure which is present in the fluid state in the presence of M NaOH (Fig. 2B) has a

#### 116 Recent Advances in Crystallography

minimum density, whereas the intermediate density rests with the detected cubic structure and finally the maximum density will be closer to the hexagonal close packing than to the simple cubic structure. This is contrary for the Lipid A-diphosphate invariant to the particle number density, *n*, and T=constant, but at very low *I* of M to mM NaCl or nM Ca2+, respectively [9, 11].

The influence of the Lipid A-diphosphate crystal-crystal-coexistence within the crystallization process has also to be considered. Since there is a noticeable variation in large and small m-sized crystals as a function of polydispersity in size and charge, the ratio may be important so that the expanded Lipid A-diphosphate crystal phase is metastabile and a function of , T and I. As a result the density of the Lipid A-diphosphate nuclei is increasing with (*n*), which is contrary of the classical nucleation theory (CNT) [60]. According to this theory the density of the crystal is the same as the bulk density, or the density decreases with increasing of the Young-Laplace pressure, c = /Lc = *g* , where Lc is the capillary length and depends on the curvatures inside and outside of the nuclei, due to capillary forces [74, 75], which takes also the surface tension and the chemical potential () into account. Thus the assumption of CNT is independent on is no longer valid. This result in a decrease of the nucleation rate with an increase in supersaturation is governed by the increase in rather by slowing down the kinetics. There is also strong evidence that the 2 d crystals of Lipid A-diphosphate do not melt in a first-order transition but may be in secondorder transition. This behavior follows the theory developed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY), which predicts that a third phase, namely the hexatic phase with short-range translational order and quasi-long-range order exists between crystal and liquid [60-64].

### **5. Conclusion**

The successful production of Lipid A-phosphate crystals makes it extremely useful to study various Lipid A-diphosphate assemblies of e.g. four, three, and penta- or hexaacylated Lipid A-phosphate approximants including those of modified disaccharide or monosaccharide moieties. This still remains to be elucidated. It was possible to construct different Wigner-Seitz polyhedra that make up the overall volume of the Frank-Kasper type unit cells with complexes comprised of Lipid A-diphosphate, antagonistic and non-toxic Lipid Aphosphate analogues depending on volume fraction, ( = 2 ·c), the nature of the counterions and temperature. They form by spontaneous self-assembly and appear to obey the principles of thermodynamically reversible self-assembly but once self-assembled strongly resist disassembly. Base on these principles, Lipid A-phosphate assemblies can be designed which form large unit cells by containing more than hundreds of Lipid Aphosphates. The range of Lipid A-phosphate structures may also be increased further by employing various different ("non-identical subunits") and identical subunits of Lipid Aphosphate in analogy with block copolymers. The rational design of such assemblies and the nucleation and creation of polymorphic Lipid A-phosphates production of mesoscopic suitable cellular networks, and structure-function relationships will be impacted by a theoretical and practical understanding of the spherical assemblies, rod-like assemblies and the mixtures thereof. Furthermore, the unit cell found for a four-single-chained Lipid Aphosphate approximant contained four honeycomb cells: two triangular and two quadrangular. However, the corresponding monophosphate contained 16 cells, of which either 10% or 66% were quadrangular. Given the theoretical and practical importance of this system, we expect that the attention given to it will substantially increase our knowledge on Lipid A-di-and monophosphates and the driving forces for the ordered assemblies. Furthermore, the structure of the Lipid A-diphosphate rod can be explained as truncated large dodecahedra.

The crystallization and phase behaviour of the Lipid A-diphosphate in two-dimensional (2d) and three-dimensional (3d) systems has been elucidated in more detail than before and analyzed as a function of , T, , morphology, and structure stability with the application of the CNT and KTHNY theories. But the experimental situation appear to be more complicated, because no real long-range translational order exists in 2d crystals and the phase behaviour close to freezing has been found to be richer than in 3d systems. We discovered for the Lipid A-diphosphate system a hexatic phase with short-rangetranslational order and quasi-long-range orientational order between crystal and liquid.
